The Port Authority is working on a hush-hush project to terror-proof the four PATH subway tunnels running under the Hudson River to thwart a potential catastrophic bombing that could flood the system, The Post has learned.

Defense contractors — toiling in the cloak of darkness — are installing reinforced metal plates along the interior walls of the tunnels, and massive flood-prevention gates are being erected at either end of the two main lines that run from the World Trade Center and the West Village to Jersey City, sources said.

The flood gates are designed to close off one or more tubes should water come surging in. That would protect other parts of the PATH system and its riders, which number about 250,000 a day.

“These are designed to avoid massive, catastrophic flooding, and the Port Authority will have protocols in place to evacuate everyone in the tunnel first,” a source said.

There is pressure on PA officials to finish the incredible, $600 million project — the World Trade Center memorial is set to open next year, and One WTC is scheduled for completion in 2013.

“They’re installing about 15 pieces of steel each night,” said a source familiar with the construction work, which happens mostly in the wee hours so that PATH service suffers minimal disruptions.

“There are iron workers in the tunnels installing what appear to be inch-thick plates,” the source added.

Part of the $600 million for the project — which was originally $900 million but was brought in under budget — was authorized by the PA in 2006.

In that same year, law-enforcement officials foiled a plot to bomb the PATH system. A terrifying report about the vulnerability of the subway’s tunnels to a bomb also was leaked to the media.

The report said that if a small explosive — with enough power to create a 50-foot hole in the tunnel — were detonated, more than a million gallons of Hudson River water each minute would surge into the tubes.

And one major, specific concern about the PATH tunnels is that they were built nearly a century ago. The four tubes — two going to the World Trade Center and two going to Greenwich Village — are essentially iron cylinders that were dug below a thick layer of mud at the bottom of the river.

Those tunnels are thought to be considerably weaker than other underground subway routes, which were bored with gigantic machines into rock.

The majority of the dollars for the PATH project come from the PA, with other money from the Department of Homeland Security and the federal stimulus, the sources said.

“The safety of our customers is the Port Authority’s highest priority, which is why we have spent over $5 billion since 9/11 upgrading the security systems at our facilities,” said Ernesto Butcher, the agency’s chief operating officer.